G.F.Zolotenko Many-valued solutions of general problem of the theory of relative fluid motion |
Applied hydromechanics, Vol. 8 (80) ¹ 1, (2006) |
| The input general problem of the theory of relative fluid motion for Laplace equation with initial and boundary conditions is reformulated as an initial-boundary value problem for the system of two equations consisting of Lagrange - Cauchy equation and Laplace equation. It is established that Lagrange - Cauchy equation for quasipotential of relative fluid motion is hyperbolic. It is shown that the free surface of a fluid is the characteristic of this form of Lagrange - Cauchy equation. The possibility of existence of many-valued solutions of a considered problem is proved and the example of such solution is given (the problem on "the flying cylinder''). Conditions of compatibility of Cauchy data on a liquid free surface considered as the characteristic are formulated. |
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| TEXT LANGUAGE: Russian |